Symmetry

by Claire Vallance

Read here Read at LibreTextsPDF

Group Theory is a branch of the mathematical field of algebra. One important application, the theory of symmetry groups, is a powerful tool for the prediction of physical properties of molecules and crystals. It is for example possible to determine whether a molecule can have a dipole moment. Many important predictions of spectroscopic experiments (optical, IR or Raman) can be made purely by group theoretical considerations.

Description from LibreTexts.

Publisher
University of Oxford
Subjects
Chemistry, Physical and Theoretical Chemistry Textbook Maps
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Chapters
  7. 1.1: Introduction to Symmetry
  8. 1.2: Symmetry Operations and Symmetry Elements
  9. 1.3: Symmetry Classification of Molecules- Point Groups
  10. 1.4: Symmetry and Physical Properties
  11. 1.5: Combining Symmetry Operations - ‘Group Multiplication’
  12. 1.6: Constructing higher groups from simpler groups
  13. 1.7: Mathematical Definition of a Group
  14. 1.8: Review of Matrices
  15. 1.9: Transformation matrices
  16. 1.10: Matrix Representations of Groups
  17. 1.11: Properties of Matrix Representations
  18. 1.12: Reduction of Representations I
  19. 1.13: Irreducible representations and symmetry species
  20. 1.14: Character Tables
  21. 1.15: Reduction of representations II
  22. 1.16: Symmetry Adapted Linear Combinations (SALCs)
  23. 1.17: Determining whether an Integral can be Non-zero
  24. 1.18: Bonding in Diatomics
  25. 1.19: Bonding in Polyatomics- Constructing Molecular Orbitals from SALCs
  26. 1.20: Calculating Orbital Energies and Expansion Coefficients
  27. 1.21: Solving the Secular Equations
  28. 1.22: Summary of the Steps Involved in Constructing Molecular Orbitals
  29. 1.23: A more complicated bonding example
  30. 1.24: Molecular Vibrations
  31. 1.25: Summary of applying group theory to molecular motions
  32. 1.26: Group theory and Molecular Electronic States
  33. 1.27: Spectroscopy - Interaction of Atoms and Molecules with Light
  34. 1.28: Summary
  35. 1.29: Appendix A
  36. 1.30: Appendix B- Point Groups
  37. Back Matter
  38. Index
  39. Glossary
  40. Detailed Licensing